Question

find the square root of x^6-4x^4-6x^3+4x^2+12x+9

Answer 1

Let $(x^{3} + bx + c)$ is square root.

$( x^{3} + bx + c)^{2} = x^{6} + 2b x^{4} + 2c x^{3} + b^{2} x^{2} + 2bcx + c^{2}$

So,
2b = -4
-> b = -2
2c = -6
-> c = -3

$( x^{3} - 2x - 3)$ is square root.